*Subjects*: Discrete dynamics*Written*: 21 December 1992*Abstract*. The emerging role of nonlinear dynamical systems theory in the sciences, both in model building and data analysis, is leading to a uniform working strategy in all fields of science. Thus, compatible models in these fields may be combined into massively complex models for whole systems, such as Gaian physiology (land, ocean, and atmosphere), human population growth and demographics, the world economy, or combinations of these. These massive models, though simpler than nature, may be too complex for our understanding. This problem is the basis for the new emphasis on scientific visualization in general, and dynamical visualization in particular. That is, given a continuous or discrete dynamical system of very high dimension, how can we visualize and understand its behavior? In this paper we will consider a special case of this problem, in which the massively complex dynamical system is a semi-cascade, that is, the iteration of non-invertible map, or endomorphism. The strategy of visualization of this system consists of projection of the trajectories onto a low-dimensional (especially, two- or three- dimensional) subspace. The new method of critical curves, discovered by Christian Mira in 1964 for the study of plane endomorphisms, provides tools to infer the behavior of the massive system from the simple observation of its projection onto a subspace.- [PDF], 388 KB, 3 pages
MS#74. Endomorphisms and Visualization, 1992
Last revised by Ralph Abraham |